English

Semistar operations and standard closure operations

Commutative Algebra 2015-12-11 v2

Abstract

Let RR be a commutative ring. It is shown that there is an order isomorphism between a popular class of finite type closure operations on the ideals of RR and the poset of semistar operations of finite type.

Keywords

Cite

@article{arxiv.1304.8067,
  title  = {Semistar operations and standard closure operations},
  author = {Neil Epstein},
  journal= {arXiv preprint arXiv:1304.8067},
  year   = {2015}
}

Comments

The main change from the previous version is a new theorem in section 4 characterizing the standardized radical in terms of the total quotient ring. I also incorporated minor changes following the referee's comments. 12 pages, comments welcome

R2 v1 2026-06-22T00:09:01.702Z